AlongTrack Moving Target Indication Algorithm in FMCW SAR
The geometry of an alongtrack moving target in a FMCW SAR system is illustrated in Fig. 5.10. In Fig. 5.10, the instantaneous slant range can be expressed as
Fig. 5.10 Geometry of an alongtrack moving target in FMCW SAR
Substitute Eq. 5.4.4 into Eq. 5.2.7, the echo of the alongtrack moving target can be presented as
The fourth term of Eq. 5.4.5 is the range walk induced by FMCW system, which is determined by the alongtrack velocity. The additional range walk is often removed as a phase error in the existing FMCW SAR GMTIm algorithms. However, it is actually a favorable factor for the moving target indication. After range compression and RCMC, the trajectories of the stationary targets are straight lines that are parallel to the azimuth direction, whereas the trajectories of the alongtrack moving targets are not parallel to the azimuth direction as a result of the residual range curvature and the additional range walk.
Hough transform was proposed by P.V.C. Hough (1962) for the image characteristic detection. It is widely used in digital image processing, especially in dealing with the straight line indication and parameter estimation. After the Hough transform, the RCM trajectories in the scene are transformed into peaks. In the Hough transform domain, the amplitudes and locations of the peaks indicate the linearity and the slopes of the RCM trajectories, respectively. Since the slopes of the trajectories of the stationary targets and the moving targets are different, the peaks are located at different locations. By differentiating the locations of the peaks, the stationary targets can be suppressed and the alongtrack moving targets can be
detected. The relationship between the angle в of Hough transform and the alongtrack velocity is
The flowchart of the proposed algorithm is shown in Fig. 5.11.
Simulated data is employed to evaluate the performance of the proposed algorithm. Three stationary targets (ST1, ST2, and ST3) and two moving target (MT1 and MT2) are set in the scene, and an alphastable distribution noise with stability parameter a equals 1.5 is added to the echo to simulate the clutter of the real FMCW SAR data. The system parameters of the typical FMCW SAR are listed in Table 5.1, and the information of the five targets is listed in Table 5.2.
Figure 5.12a shows the results of the Hough transform after the azimuth downsampling and the range interpolation. The downsampling rate and range interpolation rate are set as 4 and 32, respectively. The larger these two parameters are, the more distinctive the residual rang walk migration will be. However, the ratio of the interpolation rate to the downsampling rate determines the data amount and calculation burden, thus the values should be chosen eclectically [20]. According to Fig. 5.12a, the peaks of the stationary targets are located at regions around в = 0° and в = 180°, and the peaks of the moving targets are located away from these regions. Figure 5.12b illustrates the result after setting the regions в = 0°5° and в = 175°180° to zeros. The spectra of the stationary targets have been suppressed, and the peaks of the moving targets are contained. The amplitude image of all the targets, which is the indication of the linearity of the trajectories, is shown in Fig. 5.12c. The amplitude peaks (tagged by the rectangles) of ST1, ST2, and ST3 are 9, 11, 7, respectively, and those of MT1 and MT2 are 24 and 21, respectively. It is noted that the amplitudes of the moving targets are larger than those of the stationary targets. The result of the CFAR detection is shown in Fig. 5.12d. We can see from Fig. 5.12d that the energy of the stationary targets is eliminated, and the moving targets MT1 and MT2 are detected.
With the result of the Hough transform, the alongtrack velocities of the moving targets can also be estimated, and in turn the targets can be focused and relocated in the stationary image. Note that before azimuth refocusing, the additional range walk of the moving target must be corrected. Figure 5.13 shows the comparison of azimuth imaging of MT1 before and after additional range walk correction. From
Fig. 5.11 Flowchart of the proposed algorithm
Table 5.1 System parameters
Parameter 
Value 
Carrier frequency 
1 x 10^{10} Hz 
Pulse repetition frequency 
500 Hz 
Pulse bandwidth 
1 x 10^{8} Hz 
Range sampling rate 
2.67 x 10^{5} Hz 
Central slant range 
1000 m 
Reference range 
600 m 
Antenna size 
1 m 
Platform velocity 
100 m s^{1} 
Fig. 5.12 Result of Hough transform, a before and b after the removal of the stationary targets. c The amplitude of peaks of the five targets after the clutter suppression. d CFAR detection results
Table 5.2 Target parameters
Target 
Slant range (m) 
Alongtrack velocity (ms^{1}) 
MT1 
1000 
10 
MT2 
900 
20 
ST1 
1200 
0 
ST2 
1100 
0 
ST3 
800 
0 
Notes MT1 and MT2 represent moving target 1 and 2, respectively. ST1, ST2, and ST3 represent stationary target 1, 2, and 3, respectively
Table 5.3 Imaging quality analysis
Target 
Range direction 
Azimuth direction 

IRW 
PSLR 
ISLR 
IRW 
PSLR 
ISLR 

(samples) 
(dB) 
(dB) 
(samples) 
(dB) 
(dB) 

MT1 
1.850 
25.320 
2.622 
3.000 
14.706 
9.830 
ST1 
1.800 
25.312 
2.556 
3.000 
14.827 
9.928 
Notes MT1 represents moving target 1, and ST1 represents stationary target 1. IRW impulse response width, PSLR peak side lobe ratio, ISLR integrated side lobe ratio
Fig. 5.13 Azimuth compression result for the target MT1
Fig. 5.13, it can be observed that the azimuth resolution is improved after the correction of the additional range walk. Detailed imaging quality between MT1 and ST1 is compared in Table 5.3. From Table 5.3, the focusing performance of the moving target is convincing since it shares the same imaging quality with stationary targets.